A triangular region is bounded by the two coordinate axes and the line given by the equation $2x + y = 6$. What is the area of the region, in square units?
Answer: To start, use the equation to solve for the $x$ and $y$ intercepts of the line.  Letting $x$ equal 0, the $y$-intercept is 6.  Letting $y$ equal 0, we find that $2x=6$ so the $x$-intercept is 3.  Using the intercepts, we can graph the line as shown: [asy]size(100,0);
fill((0,0)--(0,6)--(3,0)--cycle,gray(.7));
add(grid(5,8));
draw((0,0)--(5,0),linewidth(2));
draw((0,0)--(0,8),linewidth(2));
label("",(5,0),E);
label("",(0,8),N);
draw((0,6)--(3,0),blue,Arrows);[/asy] We wish to find the area of the shaded region.  This is a right triangle with one base of length 3, and one of length 6.  Therefore, the area is equal to $\frac{1}{2}\cdot 3\cdot 6=\boxed{9}$.